Solve r*9x^2-12x+4=0

$$r \cdot 9 x ^ { 2 } - 12 x + 4 = 0$$

Solve for r

$$r=-\frac{4\left(1-3x\right)}{9x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add 12x to both sides. Anything plus zero gives itself.

$$r\times 9x^{2}+4=12x$$

Subtract 4 from both sides.

$$r\times 9x^{2}=12x-4$$

The equation is in standard form.

$$9x^{2}r=12x-4$$

Divide both sides by 9x^{2}.

$$\frac{9x^{2}r}{9x^{2}}=\frac{12x-4}{9x^{2}}$$

Dividing by 9x^{2} undoes the multiplication by 9x^{2}.

$$r=\frac{12x-4}{9x^{2}}$$

Divide 12x-4 by 9x^{2}.

$$r=\frac{4\left(3x-1\right)}{9x^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\left(\sqrt{1-r}+1\right)}{3r}\text{; }x=\frac{2\left(-\sqrt{1-r}+1\right)}{3r}\text{, }&r\neq 0\text{ and }r\leq 1\\x=\frac{1}{3}\text{, }&r=0\end{matrix}\right.$$